A261556 Numbers that divide the sum of the product of the factorials of their digits and the sum of the factorials of their digits.
1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 17, 54, 86, 573, 768, 999, 6143, 94584, 159287, 27167549, 40548073, 72382636, 131092614, 340720926, 1161216721, 2955383683, 3892089702, 5304046976, 6554754648, 72338498624, 279445396448, 331043595868, 466026097373, 962499474063, 3082891291712
Offset: 1
Examples
54 is in the list because 5! = 120, 4! = 24, 120*24=2880, 120+24=144, 2880+144=3024, 3024/54=56.
Programs
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Mathematica
fQ[n_] := Block[{d = IntegerDigits[n]!}, Mod[Times @@ d + Total@ d, n] == 0]; Select[Range@ 1000000, fQ] (* Michael De Vlieger, Aug 26 2015 *) -
PARI
isok(n) = my(d = digits(n)); ((sum(k=1,#d, d[k]!)+prod(k=1,#d, d[k]!)) % n) == 0; \\ Michel Marcus, Aug 25 2015
Extensions
a(24)-a(25) from Jon E. Schoenfield, Aug 24 2015
a(26)-a(30) from Giovanni Resta, Aug 26 2015
a(31)-a(34) from Chai Wah Wu, May 04 2019
a(35) from Giovanni Resta, Aug 19 2019